where \(f_{k}^{\lambda }(I_b) = ||\hat{\xi }^{\lambda }_{k}({I_b})||_1\)  for the randomised adaptive Lasso. The extension to the randomised adaptive group Lasso simply requires \(f_{k}^{\lambda }(I_b) = ||\hat{\xi }^{\lambda }_{k}({I_b})||_2\) . Second, by computing the probabilities of being selected over a given range of \(\lambda \) 's the stability paths can be obtained. That range is initially denoted \(\Lambda = [\epsilon \lambda _{max}; \lambda _{max}]\) , where \(\epsilon \)  is the path length and \(\lambda _{max}\)  is the regularisation parameter where all coefficients \(\hat{\xi }\)  are null. [1]} derive an upper bound on the expected number of false positives \(\mathbb {E}(V)\) , that can help determining a smaller \(\Lambda \)  region where some control on the selection error can be warrantied. By fixing this bound to \(EV_{max}\) , the regularisation region becomes,
\(\Lambda ^* = \left\lbrace \lambda \in \Lambda \text{ such that, } \mathbb {E}(V) \le \frac{q_\Lambda ^2}{(2\pi _{thr}-1)p} \le EV_{max} \right\rbrace \) 
